2.4 Machine learning algorithms
2.4.1 Support vector machine (SVM)
SVM has developed from the optimal classification surface in linearly separable cases, and based on statistical learning theory, it has excellent generalization ability in machine learning by replacing the empirical risk minimization principle with the structural risk minimization principle (Araghinejad, 2013) .By introducing appropriate inner product kernel functions, the samples in the input space can be mapped to high-dimensional spaces, thereby achieving linear classification or regression after a certain nonlinear transformation without increasing computational complexity (see Figure 5 (a)). When SVM is applied to regression problems, its learning goal is to find the best hyperplane closest to all data points at a given interval. Given the dataset {(x1. y1), (x2. y2), …, (xi, yi)}, the problem can be converted into an optimization problem under given objective functions and constraint which shows as followed:
Where, and b are the weight coefficients and bias coefficients of the optimal hyperplane respectively. C is the penalty factor, 、 are introduced slack variables; is the given interval (ARNARI S, 1999; Choubin et al., 2018; VAPNIK V, 1997) .